Time-dependent probability density function for general stochastic logistic population model with harvesting effort

2021 ◽  
pp. 125931
Author(s):  
Olusegun Michael Otunuga
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Population Model ◽  
Time Dependent ◽  
Dependent Probability ◽  
General Stochastic

A probability density function method for turbulent mixing and combustion on three-dimensional unstructured deforming meshes

2000 ◽  
Vol 1 (2) ◽  
pp. 171-190 ◽  
Author(s):  
S Subramaniam ◽  
D. C. Haworth
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Turbulent Mixing ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Particle Number Density ◽  
Time Dependent ◽  
Ic Engine ◽  
Density Control

A hybrid Lagrangian-Eulerian methodology is developed for numerical simulation of turbulent mixing and combustion in arbitrary three-dimensional time-dependent geometric configurations. The context is a probability density function (PDF) based approach intended for modelling in cylinder processes in reciprocating piston internal combustion (IC) engines. Issues addressed include mean estimation, particle tracking and particle number-density control on three-dimensional unstructured deforming meshes. The suitability of the methodology for statistically time-dependent three-dimensional turbulent flow with large density variations is demonstrated via simulations of turbulent freon vapour/air mixing on an unstructured deforming mesh representing an idealized IC engine [13]. Computed profiles of mean and r.m.s. freon mole fractions show good quantitative agreement with measurements. Moreover, inherent advantages of the Lagrangian-Eulerian PDF approach are demonstrated, compared to Eulerian finite volume solutions of an (approximately) equivalent set of moment equations. The new approach is, by design, compatible with existing computational fluid dynamics codes that are used for multidimensional modelling of in-cylinder thermal fluids processes. This work broadens the accessibility of PDF methods for practical turbulent combustion systems.

The cost of a carrier-borne epidemic

1974 ◽  
Vol 11 (4) ◽  
pp. 642-651 ◽  
Author(s):  
D. Jerwood
Keyword(s):  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Density Function ◽  
Expected Number ◽  
Stochastic Epidemic ◽  
Definition Of ◽  
The Cost ◽  
General Stochastic

In this paper, the cost of the carrier-borne epidemic is considered. The definition of duration, as used by Weiss (1965) and subsequent authors, is generalised and the probability distribution for the number of located carriers is obtained. One component of cost, namely the area generated by the trajectory of carriers, is examined and its probability density function derived. The expected area generated is then shown to be proportional to the expected number of carriers located during the epidemic, a result which has an analogue in the general stochastic epidemic.

Nonstationary Response Envelope Probability Densities of Nonlinear Oscillators

2006 ◽  
Vol 74 (2) ◽  
pp. 315-324 ◽  
Author(s):  
P. D. Spanos ◽  
A. Sofi ◽  
M. Di Paola
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Planck Equation ◽  
Nonlinear Oscillators ◽  
Basis Functions ◽  
Time Dependent ◽  
Fokker Planck Equation ◽  
Response Envelope ◽  
Fokker Planck

The nonstationary random response of a class of lightly damped nonlinear oscillators subjected to Gaussian white noise is considered. An approximate analytical method for determining the response envelope statistics is presented. Within the framework of stochastic averaging, the procedure relies on the Markovian modeling of the response envelope process through the definition of an equivalent linear system with response-dependent parameters. An approximate solution of the associated Fokker-Planck equation is derived by resorting to a Galerkin scheme. Specifically, the nonstationary probability density function of the response envelope is expressed as the sum of a time-dependent Rayleigh distribution and of a series expansion in terms of a set of properly selected basis functions with time-dependent coefficients. These functions are the eigenfunctions of the boundary-value problem associated with the Fokker-Planck equation governing the evolution of the probability density function of the response envelope of a linear oscillator. The selected basis functions possess some notable properties that yield substantial computational advantages. Applications to the Van der Pol and Duffing oscillators are presented. Appropriate comparisons to the data obtained by digital simulation show that the method, being nonperturbative in nature, yields reliable results even for large values of the nonlinearity parameter.

The cost of a carrier-borne epidemic

1974 ◽  
Vol 11 (04) ◽  
pp. 642-651 ◽  
Author(s):  
D. Jerwood
Keyword(s):  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Density Function ◽  
Expected Number ◽  
Stochastic Epidemic ◽  
Definition Of ◽  
The Cost ◽  
General Stochastic

In this paper, the cost of the carrier-borne epidemic is considered. The definition of duration, as used by Weiss (1965) and subsequent authors, is generalised and the probability distribution for the number of located carriers is obtained. One component of cost, namely the area generated by the trajectory of carriers, is examined and its probability density function derived. The expected area generated is then shown to be proportional to the expected number of carriers located during the epidemic, a result which has an analogue in the general stochastic epidemic.

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